•Low-cost photoreactor design concept for solar-driven synthesis•High photocatalytic efficiency throughout the day and year without sun tracking•Concise design guideline for facile photoreactor dimensioning Technologies replacing fossil energy carriers are essential for ways into a sustainable future. Therefore, solar fuels and carbon feedstocks, synthesized from carbon dioxide and water enabled by sunlight, are the subjects of substantial research and development efforts. This work advances the field by introducing a low-cost photoreactor design for solar-driven synthesis. The introduced photoreactors have a low level of complexity, are readily manufacturable via mass fabrication techniques in polymers, and are easy to adapt to diverse photocatalysts. Further, the photoreactors master the two-faceted engineering challenge of (1) guaranteeing operating conditions under which the quantum yield of the photocatalyst peaks and (2) ensuring a high efficiency of radiation transport from the photoreactor aperture to the photocatalyst. The resulting key feature is a photon/energy efficiency that is high throughout the day and year without the need to employ sun tracking. Solar-driven photocatalytic processes are an emerging field that inspires hopes and dreams of a sustainable future on planet Earth. Using carbon dioxide and water as feedstocks, photocatalytic processes could deliver the energy and carbon feedstock for the future world economy. However, until today, low achieved photocatalytic efficiencies and high costs of photoreaction technology are hurdles for photocatalytic processes at scale. Within this contribution, a low-cost, milli-to-micro structured, and panel-like photoreactor concept, which is suitable for small-scale decentral and large-scale solar farm applications, is introduced. The key feature is a high achieved photocatalytic efficiency at a low design complexity and system cost. The optical modeling and analysis reveal achievable limits and prevalent loss mechanisms cumulating in a concise design guideline for the proposed photoreactors. The guideline comprehensibly establishes a connection between design parameters and performance metrics at a universal level, thereby providing a basis for adaptation and further development in the field of solar-driven photosynthesis. Solar-driven photocatalytic processes are an emerging field that inspires hopes and dreams of a sustainable future on planet Earth. Using carbon dioxide and water as feedstocks, photocatalytic processes could deliver the energy and carbon feedstock for the future world economy. However, until today, low achieved photocatalytic efficiencies and high costs of photoreaction technology are hurdles for photocatalytic processes at scale. Within this contribution, a low-cost, milli-to-micro structured, and panel-like photoreactor concept, which is suitable for small-scale decentral and large-scale solar farm applications, is introduced. The key feature is a high achieved photocatalytic efficiency at a low design complexity and system cost. The optical modeling and analysis reveal achievable limits and prevalent loss mechanisms cumulating in a concise design guideline for the proposed photoreactors. The guideline comprehensibly establishes a connection between design parameters and performance metrics at a universal level, thereby providing a basis for adaptation and further development in the field of solar-driven photosynthesis. Solar-driven photocatalysis is an emerging research field with various envisaged application scenarios.1Ahmed S.N. Haider W. Heterogeneous photocatalysis and its potential applications in water and wastewater treatment: a review.Nanotechnology. 2018; 29342001https://doi.org/10.1088/1361-6528/aac6eaCrossref Scopus (321) Google Scholar,2Takata T. Jiang J. Sakata Y. Nakabayashi M. Shibata N. Nandal V. Seki K. Hisatomi T. Domen K. Photocatalytic water splitting with a quantum efficiency of almost unity.Nature. 2020; 581: 411-414https://doi.org/10.1038/s41586-020-2278-9Crossref PubMed Scopus (823) Google Scholar,3Uekert T. Pichler C.M. Schubert T. Reisner E. Solar-driven reforming of solid waste for a sustainable future.Nat. Sustain. 2021; 4: 383-391https://doi.org/10.1038/s41893-020-00650-xCrossref Scopus (92) Google Scholar,4Schäppi R. Rutz D. Dähler F. Muroyama A. Haueter P. Lilliestam J. Patt A. Furler P. Steinfeld A. Drop-in fuels from sunlight and air.Nature. 2022; 601: 63-68https://doi.org/10.1038/s41586-021-04174-yCrossref PubMed Scopus (80) Google Scholar In addition to implying a huge carbon dioxide utilization potential, solar-driven photocatalytic conversion of carbon dioxide and water can be an essential building block in pathways that lead toward the goals of the Paris agreement.5UNFCCThe Paris Agreement. United Nations, 2015Google Scholar However, until today, no solar-driven photocatalytic process that uses carbon dioxide and water as feedstock has been implemented at a significant scale. The challenges faced, on the one hand, are low photocatalytic efficiencies,6Wang Q. Pornrungroj C. Linley S. Reisner E. Strategies to improve light utilization in solar fuel synthesis.Nat. Energy. 2022; 7: 13-24https://doi.org/10.1038/s41560-021-00919-1Crossref Scopus (55) Google Scholar,7Pinaud B.A. Benck J.D. Seitz L.C. Forman A.J. Chen Z. Deutsch T.G. James B.D. Baum K.N. Baum G.N. Ardo S. et al.Technical and economic feasibility of centralized facilities for solar hydrogen production via photocatalysis and photoelectrochemistry.Energy Environ. Sci. 2013; 6: 1983-2002https://doi.org/10.1039/c3ee40831kCrossref Scopus (988) Google Scholar typically around 1% from an energetic point of view,4Schäppi R. Rutz D. Dähler F. Muroyama A. Haueter P. Lilliestam J. Patt A. Furler P. Steinfeld A. Drop-in fuels from sunlight and air.Nature. 2022; 601: 63-68https://doi.org/10.1038/s41586-021-04174-yCrossref PubMed Scopus (80) Google Scholar,8Nishiyama H. Yamada T. Nakabayashi M. Maehara Y. Yamaguchi M. Kuromiya Y. Nagatsuma Y. Tokudome H. Akiyama S. Watanabe T. et al.Photocatalytic solar hydrogen production from water on a 100-m2 scale.Nature. 2021; 598: 304-307https://doi.org/10.1038/s41586-021-03907-3Crossref PubMed Scopus (388) Google Scholar and, on the other hand, are high costs for the specialized photoreaction technology employed.6Wang Q. Pornrungroj C. Linley S. Reisner E. Strategies to improve light utilization in solar fuel synthesis.Nat. Energy. 2022; 7: 13-24https://doi.org/10.1038/s41560-021-00919-1Crossref Scopus (55) Google Scholar,7Pinaud B.A. Benck J.D. Seitz L.C. Forman A.J. Chen Z. Deutsch T.G. James B.D. Baum K.N. Baum G.N. Ardo S. et al.Technical and economic feasibility of centralized facilities for solar hydrogen production via photocatalysis and photoelectrochemistry.Energy Environ. Sci. 2013; 6: 1983-2002https://doi.org/10.1039/c3ee40831kCrossref Scopus (988) Google Scholar,9Braham R.J. Harris A.T. Review of major design and scale-up considerations for solar photocatalytic reactors.Ind. Eng. Chem. Res. 2009; 48: 8890-8905https://doi.org/10.1021/ie900859zCrossref Scopus (170) Google Scholar Optimizing a solar-driven photocatalytic process with respect to the achieved photocatalytic efficiency is a multi-discipline task at the interface of material sciences, optics, and chemical engineering.6Wang Q. Pornrungroj C. Linley S. Reisner E. Strategies to improve light utilization in solar fuel synthesis.Nat. Energy. 2022; 7: 13-24https://doi.org/10.1038/s41560-021-00919-1Crossref Scopus (55) Google Scholar,7Pinaud B.A. Benck J.D. Seitz L.C. Forman A.J. Chen Z. Deutsch T.G. James B.D. Baum K.N. Baum G.N. Ardo S. et al.Technical and economic feasibility of centralized facilities for solar hydrogen production via photocatalysis and photoelectrochemistry.Energy Environ. Sci. 2013; 6: 1983-2002https://doi.org/10.1039/c3ee40831kCrossref Scopus (988) Google Scholar,10Dong Y. Duchesne P. Mohan A. Ghuman K.K. Kant P. Hurtado L. Ulmer U. Loh J.Y.Y. Tountas A.A. Wang L. et al.Shining light on CO2: from materials discovery to photocatalyst, photoreactor and process engineering.Chem. Soc. Rev. 2020; 49: 5641-6114https://doi.org/10.1039/d0cs00597eCrossref Scopus (40) Google Scholar The keys to success are two core elements. First, it is a materials challenge. The quantum yield of the employed photocatalyst, defined in accordance to the recommendation by the International Union of Pure and Applied Chemistry (IUPAC), Equation 2, must be high in the photon-rich, visible band of the sunlight’s spectrum.11Fabian D.M. Hu S. Singh N. Houle F.A. Hisatomi T. Domen K. Osterloh F.E. Ardo S. Particle suspension reactors and materials for solar-driven water splitting.Energy Environ. Sci. 2015; 8: 2825-2850https://doi.org/10.1039/C5EE01434DCrossref Google Scholar Second, and of utmost importance, it is a technology challenge. It requires photoreactors that enable high photocatalytic efficiencies, or, in other words, reliably provide operating conditions under which the quantum yield peaks, and, most importantly, ensure a high radiation transport efficiency from the reactor aperture to the reaction volume.9Braham R.J. Harris A.T. Review of major design and scale-up considerations for solar photocatalytic reactors.Ind. Eng. Chem. Res. 2009; 48: 8890-8905https://doi.org/10.1021/ie900859zCrossref Scopus (170) Google Scholar,12Bala Chandran R. Breen S. Shao Y. Ardo S. Weber A.Z. Evaluating particle-suspension reactor designs for Z-scheme solar water splitting via transport and kinetic modeling.Energy Environ. Sci. 2018; 11: 115-135https://doi.org/10.1039/C7EE01360DCrossref Google Scholar Non-constant quantum yields that decrease with increasing process intensity, like that revealed, for instance, in Kant et al.,13Kant P. Trinkies L. Gensior N. Domenik F. Michael R. Geoffrey Alan O. Roland D. Isophotonic photoreactor for the precise determination of quantum yields in gas, liquid, and multi-phase photoreactions.Chem. Eng. J. 2023; 452139204https://doi.org/10.1016/j.cej.2022.139204Crossref Scopus (4) Google Scholar thereby, represent a special challenge. To guarantee a high photocatalytic efficiency in such systems, photon absorption must be homogeneous throughout the reaction volume. Photoreactors for solar-driven synthesis, which are low-cost both in fabrication and operation, (1) would be based on cheap materials,7Pinaud B.A. Benck J.D. Seitz L.C. Forman A.J. Chen Z. Deutsch T.G. James B.D. Baum K.N. Baum G.N. Ardo S. et al.Technical and economic feasibility of centralized facilities for solar hydrogen production via photocatalysis and photoelectrochemistry.Energy Environ. Sci. 2013; 6: 1983-2002https://doi.org/10.1039/c3ee40831kCrossref Scopus (988) Google Scholar,9Braham R.J. Harris A.T. Review of major design and scale-up considerations for solar photocatalytic reactors.Ind. Eng. Chem. Res. 2009; 48: 8890-8905https://doi.org/10.1021/ie900859zCrossref Scopus (170) Google Scholar,11Fabian D.M. Hu S. Singh N. Houle F.A. Hisatomi T. Domen K. Osterloh F.E. Ardo S. Particle suspension reactors and materials for solar-driven water splitting.Energy Environ. Sci. 2015; 8: 2825-2850https://doi.org/10.1039/C5EE01434DCrossref Google Scholar such as polymers, (2) would, therefore, operate under mild process conditions, (3) would not employ mechanical sun tracking,9Braham R.J. Harris A.T. Review of major design and scale-up considerations for solar photocatalytic reactors.Ind. Eng. Chem. Res. 2009; 48: 8890-8905https://doi.org/10.1021/ie900859zCrossref Scopus (170) Google Scholar,14Apostoleris H. Stefancich M. Chiesa M. Tracking-integrated systems for concentrating photovoltaics.Nat. Energy. 2016; 116018https://doi.org/10.1038/nenergy.2016.18Crossref Scopus (70) Google Scholar and (4), in the best case, would be modular to be ready for mass production and to adapt to various use cases. In analogy to the cost challenges faced within the field of high-efficiency, multi-junction photovoltaics,14Apostoleris H. Stefancich M. Chiesa M. Tracking-integrated systems for concentrating photovoltaics.Nat. Energy. 2016; 116018https://doi.org/10.1038/nenergy.2016.18Crossref Scopus (70) Google Scholar the amount of photocatalyst employed in a photoreactor should be minimized by means of smart optical design that increases the use of catalysts to a maximum. A homogeneous illumination of the whole reaction volume, consequently, should be sought. Herein, a concept for low-cost, high-efficiency, and modular milli-to-micro-structured photoreactors for solar-driven synthesis is introduced. The panel-like photoreactors are intended for use in both small-scale decentral applications (see Figure 1), as well as in solar farms. The design method and base design are applicable to any sunlight-harvesting liquid, gas, or heterogeneous multi-phase photocatalytic system. To ensure comparability with other approaches, however, the design method and the resulting photoreactor are demonstrated experimentally with the established, commercially available, and reliable potassium iron(III) oxalate photocatalytic system. The subsequent analysis reveals theoretical limits for the achievable photocatalytic efficiency within the proposed photoreactors and their dependency on material properties. The detailed loss mechanism analysis that is presented further outlines the design optimization strategies. The derived understanding of achievable limits and loss mechanisms together lead to a concise design guideline for the proposed photoreactors. The guideline connects basic design parameters with performance metrics at a universal level and, thereby, paves the way for various adaptations of the proposed design and optimization approach, even by non-experts in the field. The base design is an extrudable array of reaction channels (see the first-level zoomed-in image in Figure 1). The cross section of a single channel comprises a V-shaped concentrator capturing light from various incident directions and guiding it into a tube-like, mirrored cavity, enclosing the reaction volume (see the second-level zoomed-in image in Figure 1). The precise shape of a single concentrator cavity channel is optimized in a way that the achieved UV-vis photocatalytic efficiency (for definition, see experimental procedures and Equation 1) is maximized. The optimization is based on a 3D optical model that employs Monte Carlo ray tracing coupled to a plug flow reactor model that maps the chemical conversion. The optimization, thus, considers the specific optical and reaction engineering properties of the employed reaction system and reactor component materials. The optimization is based on a two-step algorithm, delivering a free-form shape. For details on the proceeding, see the experimental procedures section. For experimental validation, the manufactured optics are included in a single-channel lab photoreactor with standard fluid connectors (see Figure 2). The yellow highlighted cross section of the single channel, thereby, corresponds to the cross section of the imagined production photoreactor presented in Figure 1. Under collimated simulated solar light perpendicular to the aperture plane (α = β = 0°, angle definitions, see Figure 2), the free-form optimized concentrator cavity channel (CAD model drawing and photograph; see Figure S14) exhibits a UV-vis photocatalytic efficiency of 5.8% for the iron(III)-to-iron(II) photon-induced redox reaction of potassium iron(III) oxalate (see the y-intercept of the bold solid line in Figure 3, left). This number represents a UV-vis photocatalytic efficiency that is more than 4 times higher than that achieved using a simple quartz glass capillary photoreactor, equal to the one used in the free-form optimized photoreactor, but not comprising any optics (see the y-intercept of the dot-dashed line in Figure 3, left). Experimentally determined UV-vis photocatalytic efficiencies agree well with the simulated data, thus underlining the reliability of the conducted simulations and the optimization result (see circles in Figure 3, left). The observed significant performance boost induced by the concentrator cavity channel results from a repeated redirection of scattered and transmitted light toward the reaction volume. Because the redirection of rays is based on reflections, the photoreactors are denoted “reflective multi-pass photoreactors.” In analogy to similar approaches in photovoltaics design,6Wang Q. Pornrungroj C. Linley S. Reisner E. Strategies to improve light utilization in solar fuel synthesis.Nat. Energy. 2022; 7: 13-24https://doi.org/10.1038/s41560-021-00919-1Crossref Scopus (55) Google Scholar the redirection of light toward the reaction volume leads to multiple ray passes that add up to the effective optical path length, thereby increasing the probability of absorption without adding to the physical dimensions of the reaction volume or the photocatalyst mass, respectively. Seen from this perspective, the geometry optimization objective is maximizing the number of ray passes through the reaction volume. At the same time, as a consequence of multiple ray passages, the whole reaction volume is reached by photons, and the use of catalysts is maximized. The achieved peak UV-vis photocatalytic efficiency of 5.8 % might seem unimpressive at first, but it corresponds to approximately 62 % of the material property-determined, theoretically achievable limit (see section “understanding the limits”). Most importantly, the proposed design shows a pronounced tolerance toward the direction of incident light. This characteristic is decisive for any low-cost, solar-driven photocatalytic process.14Apostoleris H. Stefancich M. Chiesa M. Tracking-integrated systems for concentrating photovoltaics.Nat. Energy. 2016; 116018https://doi.org/10.1038/nenergy.2016.18Crossref Scopus (70) Google Scholar With the proposed concentrator cavity channels statically aligned with an East-West axis and the reactor aperture normal statically oriented toward the sun path at equinox, the achieved UV-vis photocatalytic efficiency is high both throughout the day and the year (Figure 3, right). This critical property allows an application without continuous mechanical sun tracking; therefore, it not only significantly reduces the capital expenditure (CAPEX) and operational expenditure (OPEX)14Apostoleris H. Stefancich M. Chiesa M. Tracking-integrated systems for concentrating photovoltaics.Nat. Energy. 2016; 116018https://doi.org/10.1038/nenergy.2016.18Crossref Scopus (70) Google Scholar but also paves the way for small-scale decentralized applications on rooftops,14Apostoleris H. Stefancich M. Chiesa M. Tracking-integrated systems for concentrating photovoltaics.Nat. Energy. 2016; 116018https://doi.org/10.1038/nenergy.2016.18Crossref Scopus (70) Google Scholar with the potential for a broad impact on the energy market.15Dittmeyer R. Klumpp M. Kant P. Ozin G. Crowd oil not crude oil.Nat. Commun. 2019; 101818https://doi.org/10.1038/s41467-019-09685-xCrossref Scopus (50) Google Scholar The advantageous incidence direction characteristic of the proposed design is a consequence of the low realized light concentration ratio (see the law of etendue conservation, explained in Smestad et al.16Smestad G. Ries H. Winston R. Yablonovitch E. The thermodynamic limits of light concentrators.Sol. Energy Mater. 1990; 21: 99-111https://doi.org/10.1016/0165-1633(90)90047-5Crossref Scopus (181) Google Scholar) of the channel cross section and the axial extension of the geometry. On a side note, the sun paths during the summer and winter solstices, depicted in Figure 2, right, highlight that the acceptance angle range, with respect to the angle α (under β = 0 °) of a statically, but optimally, oriented channel-like photoreactor, does not need to be higher than ±23.5 ° to be operational throughout the day and year.14Apostoleris H. Stefancich M. Chiesa M. Tracking-integrated systems for concentrating photovoltaics.Nat. Energy. 2016; 116018https://doi.org/10.1038/nenergy.2016.18Crossref Scopus (70) Google Scholar This design requirement directly results from the obliquity of the ecliptic of 23.5 °. Literature-standard photoreactors, for instance, tube bundle or panel photoreactors, have higher acceptance angle ranges than the introduced reflective multi-pass photoreactors. Consequently, on the one hand, they perform more homogeneously throughout the year, but, on the other hand, achieve significantly lower photocatalytic efficiencies. Importantly, in an all-year average, the introduced reflective multi-pass photoreactors outperform tube-bundle and panel-like photoreactors (see the supplemental information section on photoreactor benchmarking). Improving the achieved photocatalytic efficiency in reflective multi-pass photoreactors is constrained from two directions. First, the spectral dependency of the quantum yield of the photocatalytic system employed sets an ultimate limit for the achievable efficiency. For the potassium iron(III) oxalate system used in this work, literature data17Montalti M. Credi A. Prodi L. Gandolfi M.T. Michl J. Balzani V. Handbook of Photochemistry. CRC/Taylor & Francis, 2020Google Scholar on the quantum yield indicate that only photons with a wavelength less than 550 nm can induce a photoreaction (see the empty circles in Figure 4, right). Only about one third of all UV-vis photons of the solar spectrum fulfill this criterium. Noteworthily, a quantum yield differing from zero is a necessary but not sufficient condition to achieve photocatalytic conversion within a photoreactor. The second necessary, obvious, but non-trivial condition is photon absorption in the reaction volume. The latter is determined by radiation transport processes shaped by the reactor geometry and the optical properties of the employed construction materials. The efficiency of radiation transport from the reactor aperture to the reaction volume in reflective, multi-pass photoreactors is constrained by inherent absorptive losses that occur when light is traveling through the reactor assembly. Although the concentrator cavity channel walls are silver coated, and the quartz glass tubing is highly transparent, each wall reflection and each pass through the quartz glass tubing reduce the share of the incident photon flux that can be absorbed within the reaction volume. However, there are optimal ray paths on which such parasitic absorption is minimized. These optimal ray paths are characterized by two critical properties. First, optimal ray paths have a long ray path segment length in the reaction volume, which reduces the number of necessary ray passes until full absorption of the ray’s photons. This reduces the number of cavity wall reflections or parasitic absorption losses on the mirror coating, respectively. Second, ideal ray paths show a high ratio between ray path segment length in the reaction volume and ray path segment length in the surrounding glass. This minimizes the effect of parasitic absorption by the glass. In a circular geometry of reaction zone and surrounding glass, ideal ray paths go through the center of the assembly (Figure 4, left). Adding up the absorption contributions through the reaction volume in an infinite series of ray passes on ideal ray paths through the assembly allows the estimation of a maximum feasible reaction volume absorption share or a maximum feasible spectral radiation transport efficiency, respectively (green area in Figure 4, right). By analogy, adding up the absorption shares of the cavity wall and quartz glass tubing leads to minimum feasible parasitic absorption shares (yellow and orange areas Figure 4, right). Importantly, the maximum/minimum absorption shares are solely determined by the characteristic dimensions of the reaction volume and glass tubing (d1 and d2, Figure 4, left) and the optical properties of the reaction volume and reactor component materials (absorption coefficients of glass and reaction volume σGlass,λ and σCat,λ, and wall reflectivity Rλ, all being wavelength dependent). For details on the mathematical derivation of the absorption shares and their dependency on geometric and material properties, please refer to the corresponding section of the supplemental information. The spectral course of the spectral radiation transport efficiency limit in Figure 4, right, reveals the importance of an appropriate choice of materials and characteristic dimensions in reflective multi-pass photoreactors. Just in the band from 450 to 500 nm, in which both the spectral flux through the reactor aperture and the quantum yield are high, the maximum feasible spectral radiation transport efficiency, or the maximum share of absorption by the reaction volume, respectively, is low (green area in Figure 4, right). This system behavior is predominantly triggered by a decrease in the absorption coefficient of the employed potassium iron(III) oxalate solution dropping over 2 orders of magnitude from approximately 109 m−1 at 400 nm to 12. 5 and 1. 0 m−1 at 450 and 500 nm, respectively (see Figure S8). As a consequence, although the reflectivity of the cavity’s coating is higher than 95 % throughout the band from 450 to 500 nm (see material data in Figure S8), absorption by the cavity wall and the quartz glass tubing will dominate the radiation transport problem for wavelengths above 450 nm. Therefore, the maximum achievable UV-vis photocatalytic efficiency in the reported system equals “only” 9.8 %, and the reported achieved 5.8% UV-vis photocatalytic efficiency translates to impressive 62% of what can be achieved in the reported system defined by its characteristic dimensions and employed materials. Beyond inherent, unavoidable parasitic absorption losses shaping the achievable limits, real systems depict further losses, explaining the deviations between what can be achieved and what is achieved. These losses are on the one hand absorptive losses induced by non-ideal ray paths with a higher than minimum absorption share of the glass tubing and cavity wall (orange ray paths depicted in Figure 4, left). On the other hand, there are losses induced by rays that leave the concentrator cavity channel after multiple internal reflections prior to full photon absorption. Thus, the losses depicted in Figure 4, right, do not show the full picture of a real system. For the reported free-form concentrator cavity channel, in the optical band above 450 nm, losses through the aperture and faces dominantly contribute to the radiation transport problem (see the blue areas in Figure 5). The number of reaction volume passes that a reflective multi-pass photoreactor can guarantee before a ray is lost through the aperture or over channel faces, thereby becoming an important characteristic for optimizing the efficiency of a reflective multi-pass photoreactor. The realistically feasible number of reaction volume ray passes in the free-form concentrator cavity channel reported in this work lies just above seven ray passes (see the asymptote of the thin solid line for increasing wavelengths or decreasing system absorption respectively, Figure 5). It is noteworthy that the necessary number of reaction volume ray passes prior to full photon absorption can lie significantly below the number of reaction volume ray passes that a design can guarantee in case the absorption on a single reaction volume ray pass is significant enough. For the free-form concentrator cavity channel, this is maintained in the optical band from the UV up to approximately 450 nm (see the thin solid line in Figure 5). Considered cumulatively, the discussion of the theoretical limits for the spectral radiation transport efficiency and the analysis of prevalent loss mechanisms in a real reflective multi-pass photoreactor allows for the derivation of a straightforward universal design guideline, supporting the materials selection and the determination of suitable characteristic dimensions in reflective multi-pass photoreactors. The guideline aims for two critical system properties. First, the materials and characteristic dimensions of the cavity, reaction volume, and surrounding glass must be chosen in a way that the achievable spectral radiation transport efficiency is high throughout the relevant optical band. The relevant band is dictated by the solar spectrum and the spectral dependency of the quantum yield in the desired photoreaction, compare Figure 4, right. On a side note, in this regard, the free-form concentrator cavity channel example presented in this work is designed sub-optimally because the achievable radiation transport efficiency limit is low in the band in which the light source irradiance and quantum yield are high (see section “understanding the limits”). Second, the materials and characteristic dimensions must be chosen in such a way that a reasonable number of reaction volume ray passes leads to a significant total share of photon absorption, meaning that the total share of the incident photon flux being absorbed by reactor components is significant. Losses over the aperture and faces such as those described in the section “analyzing loss mechanisms” are minimized under this condition. For the free-form concentrator cavity channel reported in this work, a “reasonable number” corresponds to less than seven ray passes (see Figure 5). At the same time, the number of ray passes necessary to achieve a significant total photon absorption share should not be below two to avoid that there are regions in the reaction volume that are not reached by any light due to the reaction volume shading itself by intense photon absorption. This condition will ensure full catalyst usage, and, thereby, reduce the amount of catalyst employed in the photoreactor to a minimum needed. Further, a minimum number of ray passages ensures that gradients in the intensity of photon absorption in the reaction volume are small. In case the quantum yield decreases with an increasing intensity of photon absorption (for instance, similar to that described in Kant et al.13Kant P. Trinkies L. Gensior N. Domenik F. Michael R. Geoffrey Alan O. Roland D. Isophotonic photoreactor for the precise determination of quantum yields in gas, liquid, and multi-phase photoreactions.Chem. Eng. J. 2023; 452139204https://doi.org/10.1016/j.cej.2022.139204Crossref Scopus (4) Google Scholar), the control of the intensity of photon absorption is a crucial aspect of a high-efficiency photoreactor. Figure 6 shows a graphical representation of the mathematics (for details, see the corresponding section of the supplemental information) behind the proposed design guideline. The depicted design map interconnects optical properties and characteristic dimensions of the critical reactor components with the achievable photocatalytic efficiency and the number of ideal ray passes necessary to guarantee the desired total share of photon absorption. For a given Napierian absorbance (assuming Beers law) of the glass tubing (y axis) and a desired design spectral radiation transport efficiency limit (color coding), the depicted lines with constant cavity wall reflectivity link the given set of reactor component material properties to a Napierian absorbance of the reaction volume (x axis) that is necessary to ensure the desired total share of photon absorption and the targeted spectral radiation transport efficiency at the same time. From the necessary Napierian absorbance of the reaction volume, the suitable characteristic dimension of the reaction volume, in the case the absorption coefficient of the reaction volume is known, can be derived. In case the characteristic dimensions of the reaction volume are fixed, the needed catalyst absorption coefficient, or catalyst concentration, can be derived. Finally, the ticks along the lines with constant cavity wall reflectivity in Figure 6 allow an estimation of the minimum number of ideal ray passes that are needed to ensure the desired total share of photon absorption. As outlined in detail, this minimum number of ray passes must be ensured by the optics around the reaction volume; thereby, it sets the requirements for the geometry of the optical components of the photoreactor to be designed. As shown above, sophisticated Monte Carlo ray tracing simulations coupled with geometry optimization tools are a promising way to address this creative challenge to find such geometries. Implementing new technologies requires economically extremely attractive approaches. Both return on investment and interest rates must be high, especially for non-established technologies that apparently bring along a high risk. For the introduced reflective multi-pass photoreactors, costs are extremely low. Being made from three polymer parts only (two fluid connectors and one optics module, see Figure 1), all produced via established mass-manufacturing techniques, the material cost of the reactor components is estimated to be in the range of 9.4 $ m−2 (see preliminary feasibility study in the supplemental information). Assumed materials are, thereby, polycarbonate for the optics module and polyethylene for the fluid connectors. The reflective layer is assumed to be a sputtered aluminum layer. Including a catalyst worth 1 million $ per ton, the material cost estimate of the photoreactor system increases to roughly 22 $ m−2. Assuming a water splitting photocatalyst with a quantum yield equal to unity in the optical band from 360 to 450 nm, the annual production of such a photoreactor can be estimated to be roughly 870 mol a−1 hydrogen plus 435 mol a−1 oxygen, which results an annual revenue of roughly 7.5 $ m−2 a−1. A linear return on investment and a 10-year interest rate would, consequently, be as high as 34 % and 24 %, respectively. Those are promising numbers. Noteworthily, they do not include the manufacturing cost of reactor components, the plant costs, or the cost of operation and therefore are only rough estimates. For further discussion, see corresponding section of the supplemental information. On a side note, the assumed photocatalyst is an optimistic but not unrealistic assumption. Both water splitting photocatalysts that show a quantum yield close to unity2Takata T. Jiang J. Sakata Y. Nakabayashi M. Shibata N. Nandal V. Seki K. Hisatomi T. Domen K. Photocatalytic water splitting with a quantum efficiency of almost unity.Nature. 2020; 581: 411-414https://doi.org/10.1038/s41586-020-2278-9Crossref PubMed Scopus (823) Google Scholar and water splitting photocatalysts that operate with photons in the blue band of visible light18Wang Q. Hisatomi T. Jia Q. Tokudome H. Zhong M. Wang C. Pan Z. Takata T. Nakabayashi M. Shibata N. et al.Scalable water splitting on particulate photocatalyst sheets with a solar-to-hydrogen energy conversion efficiency exceeding 1.Nat. Mater. 2016; 15: 611-615https://doi.org/10.1038/nmat4589Crossref PubMed Scopus (1117) Google Scholar are already reported. Low-cost and high-efficiency photoreactors are the essential keys to the success of solar-driven photosynthesis. Within this work, a concept for modular, milli-to-micro structured photoreactors, which ensure sufficiently high photocatalytic efficiency without the need for sun tracking and with low cost in fabrication and operation, is introduced. The proposed design guideline for the general dimensioning of reflective multi-pass photoreactors takes into consideration all major design parameters and facilitates the adaptation and further development of the design approach by researchers and engineers in the field of photocatalysis and photoreaction engineering. Although the introduced design and optimization approaches are showcased with an exemplary photocatalytic system, the strength of the approach and optimization strategy is its adaptability to any liquid phase or gas phase that is a heterogeneously catalyzed photocatalytic system. However, future work must address the extension of the design guideline to photocatalysts that scatter light in addition to absorbing it.
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